A "change of basis" is an action performed in linear algebra, whereby a change in fundamental structure yields an entirely new viewpoint. This blog began as a record of a pedagogical change of basis for me, and continues as an ongoing account of my thoughts as I design and direct courses in mathematics at the University of North Carolina, Asheville.

Sunday, August 28, 2011

One of the issues we on the Curriculum Review Task Force are facing as we go about our business is the rather ill-defined identity of UNC Asheville as a university. We're finding it difficult to put a pin on our strengths, weaknesses, and other salient characteristics. What is it that best defines us, our commitment to undergraduate research? Our emphasis on service learning? Our small class sizes and opportunities for one-on-one teacher/student interaction? These all play a role, but it's becoming more and more evident that certain unintentional, often demographic, institutional characteristics shape our school more than these do.

Foremost among them is the predominance of transfer students at UNCA. Roughly half of those students graduated from UNC Asheville in any given year spent only half of their undergraduate careers at this school. Many transferred in after spending time at one or more regional community colleges, while others have bounced around from school to school, sometimes visiting as many as six or seven schools (in extreme cases) before coming here. These students often have more "real-world" experience than their peers who matriculated at UNCA as first-year students, and in any case they almost invariably contribute rich multifaceted perspectives to every class they attend. (In my experience many UNCA students with a community college background are "nontraditional" students, returning to school after several years in the workforce and several years of growing up. These students are mature, organized, diligent, and earnest about their learning. Even when they're not as "book smart" as some of the kids fresh out of high school, these other strengths more than make up for that shortcoming and make them fantastic students.)

Moreover, these students' presence has a profound impact on the structure of our curriculum. Consider, for instance, students' completion of the ILS requirements. A number of those students coming in from community colleges may arrive having completed the 44-hour core, an articulation agreement that suffices to knock out most ILS requirements; many other such transfer students, as well as those who've bounced around from school to school before landing at UNCA, have not completed the core and may arrive with little more than a long list of elective courses, numerous ILS core requirements outstanding. These students may therefore end up having to take three or four years at UNCA to complete their degree requirements, despite having spent two or three years elsewhere, and once done they may have taken as many 160, 170, or more credit hours, well more than the 140 beyond which tuition costs half again as much. (Every hour past 140 hours costs 150% the base tuition rate.)

Thus these students take a disproportionately long time to graduate, pay more for the privilege of enrollment, and often fail to see the point of the school's liberal arts mission in the first place. To this last point: many of these students come to UNCA because it's relatively cheap, it's convenient (Asheville's mild climate, high quality of life, and welcoming atmosphere make it a destination for many), and they believe it will provide them with the skills needed to fulfill the functions of whatever career they aspire to. Few transfer students come here specifically because of the interdisciplinary learning experience UNCA purports to offer through its liberal arts curriculum. More often, such students are annoyed by the burdensome requirements that curriculum imposes upon them. "I just want to take my major courses and get out of here."

Surely these students can't help but feel like suckers, stuck playing a game in which every hand is stacked against them. Yet, as I mentioned above, these students make up, and, indeed, for a long time have made up, a large percentage of our undergraduate population. (In each of the AYs 1995-6, 1998-9, 2004-5, and 2005-6, they accounted for a larger percentage of the graduating classes than "native" students did.) This isn't likely to change, given our status as a relatively low-cost provider of a fairly high-quality education.

How, then, can we restructure our curriculum to avoid treating these students like second-class citizens? For one thing, we should ensure that whatever core requirements we impose, they can be efficiently and effectively completed by all students, without sacrificing their goal of providing an authentic interdisciplinary learning experience. We should also take care to structure our major and degree programs flexibly, permitting students to fulfill these programs' requirements in a timely fashion and not get mired down by labyrinthine class sequences in which key courses are offered no more than once every year or every other year.

These are, in fact, among the principles which have been guiding our work on CRTF this summer. Time will tell if we succeed.

Students, what's your take? We've solicited woefully little input from students as we've begun our review, and I'm curious to know what you all see as the strengths and shortcomings of UNCA's curriculum. Feel free to comment.

Saturday, August 27, 2011

I've mentioned a few times (see here) the ongoing work of UNC Asheville's relatively new Curriculum Review Task Force, on which I'm serving as "point person" for the Curricular Sustainability Subgroup. We've spent the summer reviewing the structure of our own curriculum, breaking it down into little bits and comparing those bits with the corresponding bits of other schools' curricula.

The first component we examined were the majors and degree programs, writ large. After finding data that suggest these programs are considerably more prescriptive (in terms of the specificity of courses required) and burdensome (in terms of the number of courses required), we compared several of the most prescriptive and burdensome programs with cognate programs at several peer institutions, including both a few other COPLAC schools and a few institutions which serve as "role models" in one way or another (Bates College and Davidson College, among others). Our initial findings were confirmed: with a profusion of highly-specialized concentrations whose completion requires, on average, a relatively hefty amount of coursework, our programs are byzantine beasts, looking more like miniature graduate programs in some regards than the sort of programs you'd expect to find at a liberal arts institution. Notably, these findings suggest that those who place the blame for high times-to-graduation on the ILS program (of whom there are many at UNCA, especially among the old guard) are at least in part misguided; the majors are just as much to blame as the general education program.

We've just begun to examine the ILS program, drawing on data produced over the last several years (from NSSE, from perceptions surveys conducted on our faculty, etc.) in order to understand what parts of the program are working and what parts need work. Although there's more data-digging to be done, my hunch is that we're merely going to end up corroborating all of the findings made in the past few years: the intensive programs are doing quite well, and though the Humanities program, the first-year and transfer seminars, and a few other less-controversial components of ILS may need a little tweaking, it's the ILS clusters that'll need to be overhauled.

Several weeks ago my colleague Tyrone, a member of my Curricular Sustainability Subgroup, noted in a meeting that we may do well to consider our curricular issues from the point of view of "choice architecture," the art of arranging options for people in ways that help them make decisions more easily and to greater benefit. To learn more, Tyrone recommended the book Nudge: Improving decisions about health, wealth, and happiness by Richard J. Thaler and Cass R. Sunstein (New Haven, CT: Yale University Press, 2008), which I picked up at our library a couple of days back. I'm about halfway through, and so far it's proving an interesting and enlightening read. It's full of the sort of observation that makes one think "well, duh, that's obvious" about something one likely wouldn't have thought of oneself. Example: how dumb is it to arrange the range elements in a square on a stovetop, while the knobs that control them are almost invariably organized in a row (pp. 83-4)? A better choice architecture would arrange to place both the elements and their respective knobs in similar geometric configurations.

To the matter of ILS clusters, how might close attention to choice architecture help us craft a more easily-navigable system of courses which still ensures that students enjoy a meaningfully integrative interdisciplinary learning experience? Right out of the book, we might keep in mind the following points:

We should expect students to err in their choices, and design our system so that those errors won't prove catastrophic. Example: the cluster program should be flexible enough for students to plug in a single missing course at the last minute if they've let it slip their minds until then.

We should give students feedback on the choices they've made in completing their course requirements. Example: our advising software DegPar goes a long way in this regard, letting students know what requirements remain to be completed at any given time. If we move toward a system in which students design their own interdisciplinary clusters (as we've discussed doing several times now), perhaps we can require students to craft reflective essays after each prospective cluster course is completed, ensuring that they understand the ways in which the courses interrelate.

We should help students produce "mappings" which help students translate the complex benefits of their choices into more easily understood terms. Example: in a sense, we do this already by presenting several prepackaged cluster options to our students; "complete any one of these clusters," we tell them, "and you're apt to receive a meaningful integrative learning experience." For instance, the title "The Science and Politics of Human Health and Illness" makes it clear that the contents of the cluster so named will give students a multifaceted perspective on issues related to health and wellness: though the courses may be complex and challenging, the cluster's name is an easy index that guides interested students to complete that particular cluster without having first to complete every course the cluster contains.

More to come on this matter. I do recommend Nudge; it's an easy read, but a useful one.

Thursday, August 25, 2011

While the REU seemed to eat up less of my time this summer, revisions on the book (to appear early in 2012 under the title Student writing in the quantitative disciplines: a guide for college faculty) and work on the Curriculum Review Task Force seemed to take up every last bit of whatever was left.

We're now four days into the Fall 2012 semester, and I already feel as though I've found a groove in Precalculus. I've not taught this course for three years, and I must say that I've been looking forward to teaching it again. I've thought a bit about how I would approach the course, I've come up with some new activities (like this one), and I'm coming at it with renewed energy. So far the class has been great. (It doesn't hurt that the department's choice of text is not catastrophically awful, like the text we'd adopted the last time I taught that course.)

We spent today motivating relations and functions, and I ended class with a low-stakes writing exercise (who, me?) asking the students to work in small groups to come up with several examples of relations or functions which have real-world relevance, expressed as "pairings" between sets of numbers. They came up with some fantastic ones, some of which could the basis for interesting statistical surveys. A sampling (all verbatim):

The decrease of the temperature paired with the increase of the elevation

The number of texts you send paired with the time spent on your phone

Pair the childhood obesity with each child's level of poverty

The profit of the lemonade stand paired with the amount of sugar used

The speed limit of an area paired with the number of car crashes in the area

The amount of wildlife disturbances compared to the average of the new developments

Pair the number of baseball ticket sales with the baseball team's winning record

Pair the profit made by jacket companies based on temperature

I'm stoked. Both sections of this class seem to be gelling already, and they're full of outgoing individuals. Already obvious "leaders" are emerging from among the ranks of those students who are unafraid to ask questions, suggest answers, and put solutions on the board before the whole class.

Abstract Algebra has yet to get into the same groove, but as yet we've only met twice, and yesterday's class meeting was dedicated to an intentionally chaotic consideration of a boatload of multiplication tables I'd asked them to construct. In asking them to analyze and explain the patterns these tables exhibit, I'm leading them to begin thinking about what salient features the most "well-structured" algebraic objects (sets equipped with a binary operation) might possess. We'll make that more explicit tomorrow when we define monoids, groups, and semigroups.

More to come soon, I promise! On CRTF (oy), on the QEP (oy oy), on many more things...